Media Storage Type : DVD-ROM
NPTEL Course Name : Numerical Solution of ODEs
NPTEL Subject Matter Expert : Prof. M.K. Kadalbajoo
NPTEL Co-ordinating Institute : IIT Kanpur
NPTEL Lecture Count : 42
Lecture Titles:
Lecture 1 - Preliminaries
Lecture 2 - Existence, Uniqueness
Lecture 3 - Stability and Asymptotic Stability
Lecture 4 - The Euler Method
Lecture 5 - Convergence of Eulerï¾’s Method
Lecture 6 - Improvement of the error bound
Lecture 7 - Stability
Lecture 8 - Higher Order Methods
Lecture 9 - Runge-Kutta Methods
Lecture 10 - Error bounds for Runge-Kutta methods
Lecture 11 - Absolute Stability for Runge-Kutta Methods
Lecture 12 - Systems of Equations
Lecture 13 - Direct Methods For Higher Order Equations
Lecture 14 - General Single Step Methods
Lecture 15 - Convergence of General One-Step Methods
Lecture 16 - Derivation of Implicit Runge-Kutta methods
Lecture 17 - Derivation of Implicit Runge-Kutta Methods (Continued...)
Lecture 18 - Multistep Methods
Lecture 19 - Multistep Methods (Continued...)
Lecture 20 - Multistep Methods (Continued...)
Lecture 21 - The local error of the formulas based on integration
Lecture 22 - Local Error of Nystrom and Milne-Simpson Methods
Lecture 23 - Multistep Methods for Special Equations of the Second Order
Lecture 24 - Special 2nd order equations (Continued...)
Lecture 25 - Linear Multistep Methods
Lecture 26 - Linear Multistep Methods (Continued...)
Lecture 27 - Consistency and Zero-Stability of Linear Multistep Methods
Lecture 28 - Convergence of Linear Multistep Methods
Lecture 29 - Necessary and Sufficient Conditions for Convergence
Lecture 30 - Absolute Stability and Relative Stability
Lecture 31 - General methods for finding intervals of absolute and relative stability
Lecture 32 - Some more methods for Absolute and Relative Stability
Lecture 33 - First order linear systems with constant coefficient
Lecture 34 - Stiffness and Problem of Stiffness
Lecture 35 - The problem of implicitness for Stiff systems
Lecture 36 - Linear multistep methods for Stiff systems
Lecture 37 - Finite Difference Methods
Lecture 38 - Analysis of Difference System
Lecture 39 - Analytic Expression of the Error
Lecture 40 - Nonlinear second order equations
Lecture 41 - Special Boundary Value Problems
Lecture 42 - Special Boundary Value Problems (Continued...)